Lab Medicine 1

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Laboratory medicine Bellelli

Informations :

Antonio. Angeloni course coordinatore

Prof Bellelli

biochimica.bio.uniroma1.it/didattica

at the end of the first semester : you can take or not

at the end of the second semester : you must take (if you pass the first one, you pass only

half)

Laboratory medicine, help you to establish diagnosis

There is no biochemistry proper its a special part of biochemistry

Chap : Statistical basis of diagnosis

You need nosography, its classification. You patient its in one box or other box.

La nosographie est ladescriptionet la classification mthodique des maladies1. Elle est

galement appele histoire de la maladie , (du grec Historia, la description ). C'est

un lment constitutif de lanosologie.

disease : pheochromocytoma : its a benign tumor of produce noradrenaline

essential hypertension

anemia : vit - B12 vitamine

hmoglobine gene : thalassimia

anemia auto immun reaction

anemia bones - fibrosis, leuconemia

There is inter individual variability and individual

Diagnosis implies to assign a patient to a group,andrequires a nosography, i.e. a

coherent and comprehensive classification of diseases (e.g. the ICD). It will never beoveremphasized that diagnosis is a complex process and that the recognition of the

disease that affects the patient under study, and its correct classification, is only the first

step. After this has been accomplished, the physician will ask why that specific patient

succumbed to that disease, and which form that specific disease has taken in that patient:

i.e. whichspecific and unique conditions are verified in each single case of disease.We

may refer to these steps of the diagnostic procedure as the first (or general) and second

(or individual) steps of diagnosis.From a historical point of view, the general perspective of

diagnosis was initially suggested by Theophyle Laennec, strongly advocated by Robert

Koch and finally formalized in modern terms by William Osler, the individual one byArchibald Garrod.

1
http://biochimica.bio.uniroma1.it/https://fr.wikipedia.org/wiki/Descriptionhttps://fr.wikipedia.org/wiki/Nosologiehttp://biochimica.bio.uniroma1.it/https://fr.wikipedia.org/wiki/Descriptionhttps://fr.wikipedia.org/wiki/Nosologie


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Because ofinterindividual variability (genetic, clinical, epidemiological) both steps of

diagnosis are based on statistics: we infer something on a single patient because we can

assign its case to a group and we know something on the group because of our previous

experience. Thusnot only the general diagnosis, but also the individual one is based on

statistical reasoning. In what follows, we shall go through some basic concepts of statistics

that have been largely dealt with in other courses.

I - Health and disease

Health is desirable condition of the organism.

Not confond to normality

Normality its just for young peoples with reference of each sexe and ages

Diagnosing a disease in a patient implies that the physician hasat least an intuitive

concept of health and disease; unfortunately a precise definition of these terms is

surprisingly difficult. I shall give here only some schematic considerations; the student may

want to consult specialized treatises (e.g. E.A. Murphy, The Logic of Medicine or G.

Canguilhem, Le Normal et le Pathologique).

Health has been defined as "the silence of the organism" or "the desirable condition of theorganism".These definitions may be made more explicit by defininghealth as the condition

of absence of suffering (absence of symptoms), long life expectancy (good prognosis), and

ability to pursue one's interests and duties (adequate functioning).

Suffering (presence of symptoms), short life expectancy (poor prognosis) or inability to

cope with one's necessities and pleasure (poor functioning), by contrast, are indicative of

the presence of a disease.

Not all these conditions should be present in every instance of disease:e.g. common cold

is a disease that causes symptoms and reduces functioning but has good prognosis;

preclinical gastric cancer is a disease that has a very poor prognosis, but it causes no

symptoms and is compatible with full functioning (until it becomes clinically evident).

Some diseases are acute and the patient experiences a sudden decrease of his or her well

being; other are long standing or congenital (present at birth). In the case of acute

diseases, thepatient is aware of the existence of a state of health and wants it to be

restored; in the other cases often there is no previous healthy state to be restored, but

some improvement may be obtained.

Subjective symptoms : the patient is aware from this symptoms

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Objective symptoms : patient not complained for, but you can see

eg : patient complained a fatigue, he cant walk as he wants to, I listen to his chest (not

normal sound) maybe respiratory disfunction = objective symptoms

urine, blood, spinal fluid

laboratory measure some parameters and you will evaluate the conditions with the

measured values of the normality

experimental value ; so its not the true value, there is an experimental errors

2 different :

random of measure its a fluctuation

systematic errors, its because of your instruments

every instruments have a calibration to zero for a systematics errors

you need to know if its a problems with the patient, or because of the errors

Distribution parameters on populations

standart deviation in population.

Experimental error, very small

Patient between blue and red : in the middle no way to know if its seek or healthy

if you have a treatment, you can treat him = if its red, it will be better and be blue,if its blue already the treatments dont have any effects

You will have multiple diagnoses, but you want one its depend if children, adults

Since the possible reasons of departure from the healthy state are numerous and

different from each other, several conditions fulfill the above definition of disease. A very

relevant dichotomy is the following: there are diseases that are sharply separated from

health, however blurred and uncertain their diagnosis may be, and diseases that are more

or less continuous with health.Examples of diseases that are sharply separated from

health are those due to genetic or to infectious causes: there may be no doubt that a

patient suffering of Down syndrome or hemophylia or tuberculosis has a disease and

belongs to a group different from that of healthy people.We may have diagnostic doubts,

e.g. a culture of the sputum resulted negative for Mycobacteria; but we have no doubts that

a group of patients suffering from M. tuberculosis infection is "different", in the sense

defined above, from a matched group of healthy individuals.

Examples of diseases that are not sharply separated from health include arterial

hypertension, atherosclerosis, many cases of hypercholesterolemia, etc.

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A patient suffering of one of these conditions is not, or may not be, a member of a

population different from that of healthy people:e.g. everybody has minor atheromatous

plaques and disease is a matter of relative severity of a widespread condition.It is

reasonable to define the former type of disease a qualitative deviation from health, the

latter a quantitative deviation.

The above reasoning has relevant consequences on diagnosis. If we suspect that our

patient has a sharply defined disease,diagnosis is an act of categorization: we must

decide whether he or she is a member of the healthy or of the sick population. On the

contrary, if we suspect that our patient has a disease that is continuous with the healthy

condition, diagnosis is a matter of assessing the gravity of his or her condition.

Health is often confused with normality. The wordnormality indicates an event that

obeys a rule (norm); in medicine the rule is statistical and normal is used as a synonimous

of "frequent" or "common".In quantitative terms, when applicable,normal means "within

two S.D. from the mean value of the parameter under consideration" and includes 95% of

the population(if the parameter is distributed as a Gaussian).

Normality in medicine is a very crude concept, useful for the physician who wants to know

whether his or her patient requires further investigation, but nothing more.The reason why

normal can be confused with healthy is simply that because of our evolutionary history, the

desirable physical condition of the organism (i.e. health) is also fit, favoured by natural

selection, and hence common. One should be aware of this concept, however, because of

a very basic reason. Natural selection favors individuals who produce healthy, fertile and

numerous children and does not care of what happens past the fertile age of life:conditions that cause suffering and death in advanced ageare not selected against. Thus,

atherosclerosis is extremely frequent in humans above forty (somewhat later in women

than in men), as are atherosclerosis-related diseases (arterial hypertension, ischemic

parenchimal damage and so on): this is an example of a condition that is statistically

"normal" and yet pathological.

II - Distributions:experimental error, homogeneous populations, heterogeneous

populations

experimental value ; so its not the true value, there is an experimental errors

2 different :

random of measure its a fluctuation

systematic errors, its because of your instruments

you need to know if its a problems with the patient, or because of the errors

Theexperimental error is defined as the difference between the result of a measurement

and the actual value of the parameter in reality(which we should presume to be knownotherwise). There are two types of experimental error,random and systematic. The

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random error is the difference one observes when a measurement of the same, unvarying,

object is repeated several times:e.g. if we measure the weight or height of a patient, we

obtain a series of values very close, yet not exactly equal, to each other.

The systematic error is usually due to incorrect calibration and regulation of the instrument

and causes the measured values to be systematically different by some (small) amount

from the actual value:e.g. if we measure the weight of a patient using a balance that has

not been zeroed correctly, we obtain a series of systematically deviated measurements.A

measurement which has small random errors has precision; one which has small

systematic errors has accuracy.

Fig.1: Errors of measure. The "true" value of the parameter (which we suppose known) is

indicated by the red line. The green curve shows the distribution of the measurements

obtained by an accurate instrument with low precision (the mean coincides with the truevalue but the random error is large). The blue curve shows the distribution of the

measurements obtained by aprecise but inaccurate instrument (the mean does not

coincide with the true value but the random error is small).

Random errors are easier to detect than systematic ones: they usuallyhave a gaussian

distribution, in which values closer to the mean are more frequent than values far from the

mean.By contrast they are more difficult to explain and to prevent than systematic ones.

Why do random errors exist at all? They have multiple subtle causes,e.g. an instrument

that is operated by electrical power may give slightly different measurements of the same

sample due to slight voltage fluctuation in the power line.There is no way and usually no

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need to eliminate random errors (provided that they are small): theonly sensible thing to

do is to repeat the measurement several times and assume the average of the

measurements as the best estimate of the true value of the parameter.

It is important to recall that the Gaussian (or bell-shaped) curve is described by two

parameters: the mean, which defines the position of its maximum and the variance (s2)

which defines its width. The variance is defined as:

s2 = (Xi - mean)2 / (n-1)

where Xi is measurement i, and n the total number of measurements.

Mean is obviously: (Xi) / n.

Systematic errors aredifficult to detect(how can we know the "actual value" of the

measured parameter if not through another measurement?),but easier than random errors

to explain and to correct, since they usually result from incorrect instrumental setup.

Theonly sensible way to detect a systematic error is to compare the readings of two (or

more) different instruments or two (or more) different methods to measure the same

parameter.E.g. we may measure the weight of a sample using two different balances; the

measurements must be repeated several times on each instrument and averaged to take

care of random errors;if the average of the measurements obtained from the first

instrument differs significantly from the average of the measurements obtained from the

second instrument then either (or both) of them has a systematic error. It is important to

eliminate or to minimize systematic errors: this can be obtained by proper calibration of the

instruments using standard samples.To estimatethe systematic error of a clinical test is not an easy task.In some casesit can

be done by preparing an artificial sample, using the most accurate and precise instruments

in our laboratory and submitting it to the standard analysis.E.g. if we measure blood

electrolytes using potentiometric methods, we can prepare a solution of the desired ion or

salt at known concentration by weight (the balance is the most precise and reliable

instrument in the lab), and submit it to the same potentiometric measure as our blood

samples. We can also add the desired ion to the blood sample (by weighting appropriate

amounts of a suitable salt) and measure its concentration (so called internal standard).

Given the importance of this matter, all clinical instruments are frequently tested again

known standards in order to check for random and systematic errors. An important point is

the following:the relevance of systematic errors is minimized if the laboratory provides its

own experimentally determined estimates of the "normal" range of the clinical parameters it

measures (very few clinical laboratories do so).The reason is that the significance of

clinical parameters is judged by comparison with their "normal" range and if both the

parameter and its range are shifted in the same direction by a common systematic error,

the significance of the measurement is not influenced by the error.

If we measure a clinical parameter in a homogeneous human population we usually find

that its values are distributed, so that it has an average value (the mean) and values close

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to the mean are more frequent than values far from it. A plot of the frequency versus the

parameter value (grouped in discrete classes of equal amplitude) yields a bell shaped

(Gaussian) curve. The width of the Gaussian curve is determined by the variance of the

parameter (or its square root, the standard deviation). A good example is the Intelligence

Quotient, IQ, that in the healthy population has mean=100 and Standard Deviation=15

(see the blue curve in the figure below):

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Fig.2: Gaussian distributions

Patient between blue and red : in the middle no way to know if its seek or healthy

if you have a treatment, you can treat him = if its red, it will be better and be blue,if its blue already the treatments dont have any effects

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It is important to state that "healthy" in this context means that the members of the sample

have no diagnosis for a disease affecting the measured parameter. Since the parameter is

distributed, and has not the same value for all members of the population (or of the group

studied) only approximately 95% of its members fall in the interval (mean - 2 S.D.) - (mean

+ 2 S.D.).

Given that both the random error of the measurement and the distribution of the parameter

in the population are Gaussian-shaped, and are simultaneously present in our sample of

measurements, how can we distinguish between the two? We can estimate the variance of

the the measurement (i.e. the amplitude of its random error) by repeating the

measurement several times on the same individual(s), and comparing it with the variance

of the population. As a general rule, the variance of the measurement in the population is

much greater than the that of the measurement on the same individual, and when dealing

with the variance of the population, we can often neglect the random error of the

measurement. The opposite case, i.e. that the variance of the population is as large as the

variance of the measurement (it can never be smaller), is very uncommon and either

indicates that the population is made up of identical members or that our instrument is too

gross to detect the differences that are present.

Why are clinical parameters distributed, rather than identical? Several factors co-

operate to this phenomenon: genetic heterogeneity of the population; environmental

causes; clinical history and the effect of previous diseases of each individual; etc. It is an

interesting question whether randomness may also result from purely probabilistic

(stochastic) effects: this has been proven in some cases (e.g. situs viscerum inversus).

The case of heterogeneous populations is somewhat more complex. Suppose that we test

a random sample of people from the healthy population and a random sample with the

same number of people from a different population, having a specific diagnosis. We end

up with two Gaussian distributions with different mean and S.D. (blue and red curve in the

figure above). If the two samples are mixed, the end result wil be a bimodal distribution,

made up by the sum of two independent Gaussian curves (green curve, shifted vertically

by 5 points to avoid superposition with the other two). E.g. in the figure above the blue

curve may refer to the distribution of the IQ in a sample of 10,000 healthy people and the

red curve to the distribution of the IQ in a sample of 10,000 people carrying the Down

syndrome. Notice that in this example the diagnosis from the karyotype is easy and very

accurate: thus we have no doubts in the assignement of each individual to his or her

group.

If we test a random sample from the human population, we shall include healthy and ill

people according to the prevalence of each disease present in the population; and since ill

people are usually much rarer than healthy, the distribution of the measured parameter will

be again bimodal or multimodal, but the Gaussian curve corresponding to the healthy

population will dominate the picture: e.g. the prevalence of all genetic defects leading to a

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mean IQ value of 50 or less is approximately 1% of the total population (see the red and

blue curves in the picture below).

Fig.3: Gaussian distributions for populations of unequal amplitude

It will be noticed that in the above discussion of homogeneous and heterogeneous

populations, the problem of the experimental error in the measurements has been

neglected: i.e. we have assumed that the random error is much smaller than the variance

of the population and have taken the parameter values obtained from the clinical laboratory

as precisely corresponding to the actual values in the patient. This assumption is usually

safe: the experimental errors in the measurements are small with respect to the variability

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of the population.E.g. most measurements of concentration of blood solutes are accurate

to within 2-3% of the actual value and when we say that the glycemia of a patient is 80

g/dL our confidence interval is in the order of 77-83 g/dL. However, not all clinical

parameters have the same accuracy and we must be aware of possible errors in their

measurement.

Two conditions are special and require specific mention i.e.: (i) measurements that affect

the value of the parameter of interest and (ii) the presence of confounding or interfering

variables.

An example of ameasurement that affects the parameter being measured is the recording

of the blood pressure.In some individuals, the act of measuring the blood pressure causes

psychological stress, and this in turn causes an autonomous response that increases the

blood pressure (so called white coat hypertension).In this case we cannot resolve random

and systematic errors of the measurement nor can we obtain a reliable estimate of the

"normal" blood pressure of the patient.The best way to operate is to find a procedure that

minimizes this effect(e.g. we can instruct the patient to measure his or her blood pressure

by himself, using an automated recorder).

Confusing variables produce a signal indistinguishable from the variable of interest.

E.g. the gravimetric measurement of oxalic acid in the urine is easily achieved by adding

calcium chloride, allowing calcium oxalate to precipitate and weighting the desiccated

precipitate on a balance.This method is precise but if the urine contains any other anion

whose calcium salt precipitates as well (e.g. phosphate) this will be confused with oxalate

and will cause the amount of the latter to be overestimated. The presence of confusing

variables should be carefully searched for, since they cause a systematic error difficult todetect; hopefully each test has a known and finite number of potential confusing variables

(in some cases zero).

Some of the clinical parameters of a disease that is sharply distinguishable from the health

condition will present a bimodal distribution in the general population: i.e. they will

distribute in a (larger) Gaussian for the healthy group and a different (smaller) Gaussian for

the sick group, even though some conditions (e.g. relative numerosities of the two groups)

may mask the bimodality (Fig.3, above). In the case of diseases which are not sharply

distinguished from the health condition, the distribution of the clinical parameters in the

population is Gaussian and unimodal, and the disease group is identified as a "tail" of the

distribution. An interesting example is that of arterial hypertension, that may be essential

(i.e. idipathic, its cause being unknown), or may be due to some identified cause (e.g.

pheochromocytoma). The corresponding distributions being as in Fig.4:

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Fig.4: Distributions of diastolic pressure in the cases of essential hypertension and

pheochromocytoma

How strong is the distinction between qualitative (i.e. sharply distinguished) and

quantitative (i.e. continuous) deviations from the condition of health? Not very much.

Indeed given that a quantitative deviation from health like essential hypertension has

genetic and environmental factors, one may imagine that in the future we shall be able to

identify precise causes and transform it into one or more sharply demarcated disease(s).

III - Certain and probable diagnoses

Up to now we have considered the possible distributions of a measurable physiological

parameter in the healthy, ill and mixed population, under the assumption that diagnosis

could be made with certainty independently of our measurement. This is rarely the case:

most often the parameter is a clue to the diagnosis, and we have to evaluate its clinical

significance.

Before going further, let us distinguish diagnoses that are (almost) certain from diagnoses

that are only probable.Some diseases are defined precisely enough to allow the physician

to establish a diagnosis that is absolutely unequivocal.

This is the case of most genetic diseases,e.g. the Down syndrome of the above example;

of most infectious diseases, in which the presence of the causing agent can be

demonstrated with certainty; of cancers, that can be ascertained bioptically; etc.

In these cases the physiological parameters we measure give an indication for a definitive

test, whose result confirms the diagnosis.

There are diseases in which an absolute diagnosis is impossibleor at least not always

possible. In generalthese diseases have no unequivocal histological or genetic marker

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(e.g. this is the case for most psychiatric diseases); moreover theircause is often unknown

and several factors may cooperate; finally their gravity and prognosis may be highly

variable (e.g. arterial hypertension). Even diseases which admit a certain and unequivocal

diagnosis may under many instances be subject to uncertainty diagnosis:e.g. a cancer

marker may be present in the blood of our patient but the tumor may be too small to be

found and subjected to biopsy.

In all these caseswe formulate a probability diagnosis, i.e. we try to assess how likely it is

that the patient is affected by a specific disease.Probability in this case estimates how

confident we are in our diagnosis: the uncertainty lies in physician, not in the body of the

patient; and we may increase our confidence by carrying out further tests.

IV - Multiples diagnoses

In somecases the patient suffers of more than a single disease and we must establish

multiple diagnoses. Since the incidence of acute diseases is usually quite low and theirduration is short, the coexistence in the same patient of two acute diseases independent of

each other is an uncommon occurrence. By contrast the coexistence of two unrelated

diseases one chronic, the other acute or both chronic is not infrequent, especially in the

elder.

If we think that the patient suffers of two diseases at the same time, it is also important to

establish whether or not they are correlated to each other:e.g. an acute episode of

measles may cause the relapse of a previously silent tuberculosis. This is due to the

temporary immunodeficiency due to measles that reduces the defences against the

colonies of Mycobacterium tuberculosis already present in the lung or elsewhere in thebody.

V - Distributions in relation to diseases

As a general rule, when a disease admits an unequivocal diagnosis, its characteristic

parameters exhibit a bimodal or multimodal distribution in the population, or, to be more

rigorous, the human population is made up of a healthy and a hill subpopulation, each with

its normal distribution of physiological parameters. The science philosopherGeorges

Canguilhemsummarized this condition with the following definition:"there is a norm for

health and one for (each) disease; and the two norms differ from each other".In these

cases the physician uses the clinical parameters to assign his patient to its characteristic

subpopulation. In the classical view of medicine, as championed by the great physician

William Osler, this assignment is the diagnosis. If and when a certainty diagnosis can be

made, the two gaussians that represent the relevant diagnostic parameter in the healthy

and ill groups are well separated from each other, with minimal or absent superposition:

e.g. all patients suffering of Down syndrome have a trisomy of chromosome 21, at least a

partial one; whereas all healthy people have no trisomy.Diseases that only admit a probability diagnosis may take two very different forms:

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(i) the relevant clinical parameter(s) have a bimodal distribution in the population, but the

separation between the ill and healthy groups is incomplete (see the figures above); or

(ii) the relevant clinical parameter(s) have a monomodal, Gaussian distribution and the

disease affects those individuals who present extreme values. An example of this condition

is hypercholesterolemia.

The former condition is more frequent.

VI - Bayesian statistics

The most common condition faced by the clinician is the following:the patient presents

some clinical parameters which are far from the mean value of the population, yet

compatible with both illness and health (absence of a specific diagnosis).Is a diagnosis

justified in his or her case? The answer to this question is a matter of probability and relies

on the theory developed by the british mathematician Thomas Bayes (1702-1786).

The textbook example of Bayes formula is the following:we have two boxes, each

containing 100 balls.

Box 1 contains 90 white and 10 red balls; box 2 contains 10 white and 90 red balls. One

ball is picked up; how likely is it to come from box 1?

This is the a priori probability and in the present case equals 50%, given that the two boxes

contain the same number of balls and each has the same probability of being picked up.

If we are told that the ball is red, can we refine our estimate? T

he answer is yes: since the ball is red, we ignore from our calculation all the white ones,

and there are only 10% probability that the ball comes from box 1: this is because thesystem contains only 100 red balls, 10 in box 1 and 90 in box 2. Our new estimate is the ex

post or post test probability. Often, we can add more tests and refine our estimate further.

How does this example compare with medicine? Imagine to be the only physician on an

island inhabited by 200 people, half of whom suffer of malaria.

90% of the people suffering of malaria have recurrent fever;

10% have not (these are the atypical cases of malaria: malignant, blackwater fever,

cerebral).

Among the people who do not have malaria only 10% have recurrent fever (e.g. because

of infection from Borrelia recurrentis).

A patient comes to your ward: how likely he is to have malaria?

The answer is the a priori probability: 50%.

He refers recurrent fever: how does your estimate change? The answer is the post test

probability: 90%.

A comparison between the two examples is as follows:

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Box 1

contains 100 balls

90 white

10 red

Group of malaria-free

is made up of 100 people

90 refer no recurrent fever (true neg.)

10 refer recurrent fever (false pos.)

Box 2

contains 100 balls

10 white

90 red

Group of malaria-sick

is made up of 100 people

10 refer no recurrent fever (false neg.)

90 refer recurrent fever (true pos.)

ex : i meet a person (an italian in roma) and i want to guess how likely to be live in roma

rome population / italian population

and we have short conversation, he have roman accent

rome with roman accent / rome population

Box 1 contains 100 balls, 90 white and 10 red

Box 2 contains 100 balls, 10 white and 90 red

Pre test : if i show you a ball, if this from box 1 or 2 - 50 % from box 1 or 2

Post test : if we say you the balls is red - 90 % from box 2

Tropical island

Group of malaria free mountains side (box 1), 90 % refer no recurrent fever and 10 % refer

recurrent fever (due to others disease)

Groupe of malaria sick on the cost (box 2), 10 % refer no recurrent fever (if you have 2

infections), 90 % refer recurrent fever

Pre test : numerical ratio of 2 box : how many malaria patient are in the population

Post test : symptoms and group : recurrent fever on the population

Group of malaria free - 90 %

Groupe of malaria sick - 10 %

recurrent fever will be a major in malaria sick, but in minority in malaria free (but it will be

consistance because of the population of malaria free)

Let's now consider a statistically more plausible, but still intuitive example: suppose that a

patient has an IQ of 55 and that the distribution of the IQ in the population is described by

the green curve in Fig.2: this patient might be an uncommon healthy individual or may

suffer of some specific disease. How can we decide? We have a population of 10,100

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individuals belonging to two groups, one of which hosts 10,000 healthy individuals, the

other is composed by 100 people suffering of some specific disease affecting the IQ. 9,950

people from the healthy group have IQ>55, and only 50 people of this group have IQ55 and 80 have IQ


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Fig.3: Position of the patient's score at test

Clearly, our example leaves something to be desired: indeed we arbitrarily divided our

population and its groups according to the rule of thumb IQ


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below the threshold; in other cases (e.g. bilirubin concentration in the blood) the presence

of illness is more likely if the parameter value is above the threshold.

As evident from Fig.3 any threshold value will include members from the healthy group

and/or exclude members of the disease group.E.g. suppose that we take IQ=55 as a

sensible threshold, implying that any individual with IQ55, who will

not be further studied and thus will not be diagnosed, and 0.05% of the members of the

healthy group, for whom a diagnosis will be uselessly searched for.

In the clinical jargon we call positive (i.e. potentially ill) all values falling on the

"unexpected" side of the chosen threshold (e.g. IQ


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Fig.4: Positive and negative test results

The existence offalse positives and false negatives is obviously unpleasant: medicine

would be simpler if we could eliminate these and unequivocally associate positive to illness

and negative to health.This occurs in the cases described above of certainty diagnoses,

and depends on a negligible or absent overlapping of the gaussian distribution of clinical

parameter values' in the healthy and disease groups. In all other condition, however false

positives and false negatives occur. By accurately deciding the threshold value we can

reduce and even abolish either false result, but at the expense of an increase of the

frequency of the other false result.E.g. in the case of the IQ we can minimize the

frequency of false negatives by increasing the threshold to IQ=80, but such a high

threshold will cause a high frequency of false positives(refer to Figs.3 and 4).

VIII - Sensitivity and specificity of test

Each clinical test should be evaluated for its diagnostic significance, keeping in to account

its ability to discriminate health and disease. Unfortunately, even if we knew exactly how

reliable our tests are, a correct evaluation of their results also requires information about

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the incidence and prevalence of the disease we are looking for in the population. The test

characteristics we consider are:

Accuracy = (true positives + true negatives) / total number of measurements.

Predictive Value (precision) = true positives / (true positives + false positives)

Negative Predictive Value = true negatives / (true negatives + false negatives)

Sensitivity = true positives / sick individuals tested = true positives / (true positives

+ false negatives)

Specificity = true negatives / healthy individuals tested = true negatives / (true

negatives + false positives)

These characteristics are not independent from each other:e.g. sensitivity and specificity

depend on the same threshold, thus one cannot increase the one without decreasing the

other. More refined correlations may be written down if one knows the prevalence of the

disease in the population:

Prevalence = number of sick individuals / total population

E.g. accuracy estimates how often the test yields a true result, be it positive or negative,

and, if the entire population (or a large random sample) has been tested, bears the

following relation to specificity and sensitivity:

Accuracy = sensitivity x prevalence + specificity x (1-prevalence)

The above formula demonstrates that, when the entire population is tested, prevalence has

a large effect on accuracy. This depends on the obvious fact that the gorups of ill and

healthy people usually differ greatly in numerosity (see above). To compensate for this

effect, we define the balanced accuracy, i.e. the accuracy the test would have if theprevalence of the disease were 0.5:

Balanced Accuracy = (sensitivity + specificity) / 2

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Date post:	12-Apr-2018
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Lab Medicine 1

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